Pairs of partially ordered sets of tame representation type
type: Item
instance of: scholarly article
title: Pairs of partially ordered sets of tame representation type
zbMATH Open document ID: 0659.16021
DOI: 10.1016/0024-3795(88)90311-4
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Let S and T be finite partially ordered sets. It is proved in the paper that the category \({\mathcal R}(S,T)\) of representations of the pair (S,T) is of tame representation type if and only if either one of the posets S, T is linearly ordered (say S is) and the disjoint union poset \(T+S-\{s\}\), where s is maximal in S, does not contain a critical Nazarova poset (1,1,1,1,1), (1,1,1,2), (2,2,3), (1,3,4), (1,2,6), (N,5), or S and T contain the poset (1,1) but neither S nor T contains a subposet of the form (1,1,1), (1,2). Here by m we mean the chain consisting of m vertices and by N we mean \(a\prec b\succ c\prec d\).
Mathematics Subject Classification ID: 16Gxx
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 4077481
zbMATH Keywords: category of representations
zbMATH Keywords: finite partially ordered sets
zbMATH Keywords: tame representation type
author: Mark Kleiner
reviewed by: Daniel Simson
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90311-4
OpenAlex ID: W1971107960
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description: scientific article; zbMATH DE number 4077481